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timurjin [86]
3 years ago
11

Prime factorization of 50

Mathematics
1 answer:
prisoha [69]3 years ago
4 0
The prime factorization of 50 is 2x5x5
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Find the volumes of the solids generated by revolving the triangle with vertices (2, 2)​, (2, 6)​, and (5, 6) about ​a) the​ x-a
Vesna [10]
  • About the x-axis (washer method):

\displaystyle\pi\int_2^5\left(6^2-\left(\frac43x-\frac23\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(20+x-x^2)\,\mathrm dx=\boxed{56\pi}

  • About the y-axis (shell method):

\displaystyle2\pi\int_2^5x\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5x(5-x)\,\mathrm dx=\boxed{36\pi}

  • About x=7 (shell method):

\displaystyle2\pi\int_2^5(7-x)\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5(35-12x+x^2)\,\mathrm dx=\boxed{48\pi}

  • About y=2 (washer method):

\displaystyle\pi\int_2^5\left((6-2)^2-\left(\frac43x-\frac23-2\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(5+4x-x^2)\,\mathrm dx=\boxed{32\pi}

7 0
3 years ago
) If the pattern shown continues, how many black keys appear on a portable keyboard with 49 white keys? Suggestion: use equivale
andriy [413]

Answer:

35

Step-by-step explanation:

Here we see 5 black keys for every 7 white keys.

So the ratio is 5:7

If we need 49 white keys, find the amount we scale the original ratio by:

    49/7 = 7

So we are scaling by a factor of 7.

The number of black keys would be 5 * the scale of 7. = 35

So there should be 35 black keys.

5 0
2 years ago
Read 2 more answers
Is it possible for three vectors of different magnitudes to add to zero?.
amid [387]

Answer:

No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.

Explanation:

The Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vectors of unequal magnitude cannot be added to give a null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.

6 0
2 years ago
Quiz 4: Solving Inequalities
san4es73 [151]

Answer:

15x+60\leq 100

Step-by-step explanation:

Let

x -----> the number of hours that the painter works

we know that

The inequality that represented this situation is equal to

15x+60\leq 100

solve for x

Subtract 60 both sides

15x\leq 100-60

15x\leq 40

Divide by 15 both sides

x\leq 40/15

x\leq 2.67\ hours

The maximum number of hours is 2

3 0
3 years ago
Which system is most easily solved by graphing and why?
inn [45]

Answer:

System A should be solved by elimination because you can easily cancel out the 3m to solve.

System B should be solved by substitution.  Since the an equation for the y value is given, you can easily substitute it into the other equation.

System C should be solved by graphing.  You don't have to worry about any slopes or intercepts to graph.  You can graph it using only whole numbers.

8 0
3 years ago
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